Peel or slice most of the skin off of the 5 peaches and remove the pit. Don't worry about being super precise with removing every bit of skin. Also remove any bruised areas and discard.
Slice the peach flesh into smaller chunks and place in a medium sized pot.
Add the sugar and water, and place on the stove. Bring the mixture to a boil.
Once boiled, turn the heat down to a simmer and use a potato masher to break down the peaches. After the peaches are pretty pulpy, remove from heat and set aside for 20-30 minutes to steep.
While the peaches are steeping, use an electric tea kettle to bring 1.7 liters of water to a boil (Or use a regular pot on the stove if you prefer).
Place teabags in a gallon pitcher. Once the water has boiled, pour it over the teabags. Let steep for 5 minutes.
Remove the teabags, and when the peach mixture is ready, use a mesh colander set over the gallon pitcher (or do this over a mixing bowl depending on the size of your equipment) and pour the peach mixture into the colander.
Let the peach syrup drain into the tea, and use a wooden spoon to help mash more peach liquid out of the pulp. Discard pulp.
Stir well, and add ice to fill the rest of the gallon pitcher. Serve when cooled, with a peach slice and sprig of mint if you like!